1. Field of the Invention
The present invention relates to a particle simulator and a method of simulating particles.
2. Related Background Art
A discrete element method (DEM), which has originated through research in civil engineering, has been applied in particle technology. Today, the method is in great demand as a numerical analysis method used to solve an extremely wide variety of problems associated with not only particles but also continuous subjects that cannot be readily treated. Many other methods of numerically tracking discrete particle motion, such as molecular dynamics (MD), lattice gas automation (LGA), and smoothed particle hydrodynamics, have also been developed, in addition to the DEM. The DEM has a wide range of application compared to the other numerical particle analysis methods because the calculation of determining interparticle forces in consideration of geometric information of the particles, such as the size and shape of the particles, and solving Newton's motion equation can be performed at high speed. Size and shape can be considered in methods, such as a discontinuous deformation analysis (DDA), other than the DEM. Unfortunately, such a method exhibits high initial calculation load, and thus, it is not practical to process a large number of particles.
Commonly known granules and powders (which are hereinafter collectively referred to as “particles”) that can actually be seen, such as sand and flour, usually includes particles of various different sizes unless special processing, such as particle-size adjustment through mesh control, is carried out (this state is referred to as a state having a “particle diameter distribution”). Such a particle diameter distribution greatly influences the homogeneity of the particle and mechanical properties, such as deformation and flow. In industries that process particles, the particle-diameter separation efficiency, the heterogeneity and mixing efficiency of particle layers due to particle size segregation, and control of transportation and filling is always problematic. Therefore, to process particles, it is critical to accurately understand how the effect of a particle diameter distribution on the overall behavior of a particle group.
Since the DEM is a method that can consider the particle size, as described above, it is understandable to use the DEM to determine the micromechanics of particles based on a particle diameter distribution. However, a decrease in the particle diameter to 1/n causes a decrease in the volume of the particle to (1/n)3. This indicates, n3 particles with reduced volume are required to fill the volume of the original particle (precisely, the number of reduced-volume particles required is less than n3 because there will be gaps between the particles, but the order of the number is the same). Therefore, a wide particle diameter distribution cannot be processed due to restrictions on the amount of computer memory and calculation time. For example, natural soil contains particles varying in size by approximately five digits, e.g., from gravels having a diameter of several centimeters to natural clay having a diameter of several microns. Under an assumption that particles of each different size group occupy the same volume, if only one particle having a maximum diameter is included, the total number of particles will be on the order of (105)3.
In the case where a particle diameter distribution is processed using the DEM, a disadvantage is imbalance of the number of contact points due to the difference in particle diameter, in addition to the problem on the number of particles. For example, if the particle diameter ratio of the maximum particle to the minimum particle is r:1, the number of minimum particle covering the surface of a maximum particle is 4(r+1)2/12, whereas the number of maximum particles filling the surface covering the surface of a minimum particle is 4(r+1)2/r2. In other words, the maximum imbalance of the number of contact points is on the order of r2:1. The imbalance in the number of contact points lead to an imbalance in the number of calculation processes performed to determine the contact forces of the particles and the amount of calculation required to determine the sum of the contact forces. Specifically, if the particle diameters are not uniform and the particle diameter ratio increases in the DEM, the number of particles increases simply due to geometric features on the diameter, and causes an imbalance in the number of contact points. As a result, the calculation load considerably increases. In addition, if a particle diameter distribution exists in the actual program for the DEM, processing of refined search of contact candidates of which the contact is to be determined and storing contact-candidate pairs causes a significantly high calculation load compared with a uniform particle size.
In response to such problems concerning a particle diameter distribution, several methods of DEM programing for increasing processing speed associated with extracting and storing contact-candidate pairs have been proposed (for example, Japanese Unexamined Patent Application Publication No. 2007-286514 (Patent Literature 1)).
Today, high speed numerical simulation using GPUs, which have a high cost performance rate compared with CPUs, is actively used. In response to this, instead of vector processing using expensive super computers, the use of high-speed algorithms for GPUs, which are inexpensive but capable of super parallel computing equivalent to vector operation, have been promoted for particle system simulation (for example, Japanese Unexamined Patent Application Publication No. 2009-69930 (Patent Literature 2)).